General Relativity And Quantum Cosmology

Einstein equivalence principle (EEP), as one of the foundations of general relativity, is a fundamental test of gravity theories. In this paper, we propose a new method to test the EEP of electromagnetic interactions through observations of black hole photon rings, which naturally extends the scale of Newtonian and post-Newtoian gravity where the EEP violation through a variable fine structure constant has been well constrained to that of stronger gravity. We start from a general form of Lagrangian that violates EEP, where a specific EEP violation model could be regarded as one of the cases of this Lagrangian. Within the geometrical optical approximation, we find that the dispersion relation of photons is modified: for photons moving in circular orbit, the dispersion relation simplifies, and behaves such that photons with different linear polarizations perceive different gravitational potentials. This makes the size of black hole photon ring depend on polarization. Further assuming that the EEP violation is small, we derive an approximate analytic expression for spherical black holes showing that the change in size of the photon ring is proportional to the violation parameters. We also discuss several cases of this analytic expression for specific models. Finally, we explore the effects of black hole rotation and derive a modified proportionality relation between the change in size of photon ring and the violation parameters. The numerical and analytic results show that the influence of black hole rotation on the constraints of EEP violation is relatively weak for small magnitude of EEP violation and small rotation speed of black holes.

We propose a Lagrangian formulation for a varying G Newtonian-like theory inspired by the Brans-Dicke gravity. Rather than imposing an {\it ad hoc} dependence for the gravitational coupling, as previously done in the literature, in our proposal the running of G emerges naturally from the internal dynamical structure of the theory. We explore the features of the resulting gravitational field for static and spherically symmetric mass distributions as well as within the cosmological framework.

Bouncing models are alternatives to inflationary cosmology that replace the initial Big-Bang singularity by a `bouncing' phase. A deeper understanding of the initial conditions of the universe, in these scenarios, requires knowledge of quantum aspects of bouncing models. In this work, we propose two classes of bouncing models that can be studied with great analytical ease and hence, provide test-bed for investigating more profound problems in quantum cosmology of bouncing universes. Our model's two key ingredients enable us to do straightforward analytical calculations: (i) a convenient parametrization of the minisuperspace of FRLW spacetimes and (ii) two distinct choices of the effective perfect fluids that source the background geometry of the bouncing universe. We study the quantum cosmology of these models using both the Wheeler-de Witt equations and the path integral approach. In particular, we found a bouncing model analogue of the no-boundary wavefunction and presented a Lorentzian path integral representation for the same. We also discuss the introduction of real scalar perturbations.

In this paper, we propose an extension of the Ricci-inverse gravity, which has been proposed recently as a very novel type of fourth-order gravity, by introducing a second order term of the so-called anticurvature scalar as a correction. The main purpose of this paper is that we would like to see whether the extended Ricci-inverse gravity model admits the homogeneous and isotropic Friedmann-Lemaitre-Robertson-Walker metric as its stable inflationary solution. However, a no-go theorem for inflation in this extended Ricci-inverse gravity is shown to appear through a stability analysis based on the dynamical system method. As a result, this no-go theorem implies that it is impossible to have such stable inflation in this extended Ricci-inverse gravity model.

We apply the Noether Symmetry Approach to point-like teleparallel Lagrangians in view to derive minisuperspaces suitable for Quantum Cosmology. Adopting the Arnowitt-Deser-Misner formalism, we find out related Wave Functions of the Universe. Specifically, by means of appropriate changes of variables suggested by the existence of Noether symmetries, it is possible to obtain the cosmological Hamiltonians whose solutions are classical trajectories interpretable as observable universes.

In this work, we take a short recap of a formal framework of the Eddington-inspired Born-Infeld (EiBI) theory of gravity and derive the point-like Lagrangian for underlying theory based on the use of Noether gauge symmetries (NGS). We study a Hessian matrix and quantify Euler-Lagrange equations of EiBI universe. We discuss the NGS approach for the Eddington-inspired Born-Infeld theory and show that there exists the de Sitter solution in this gravity model.

A new modification of spherically symmetric models inspired by loop quantum gravity has recently been introduced by Benitez, Gambini and Pullin, who claimed that it preserves general covariance. This claim is shown here to be incorrect, based on methods of effective line elements. The same methods imply that the only novel physical effect introduced by the modification is the presence of time-reversal hypersurfaces between classical space-time regions.

We consider non-linear plane gravitational waves as propagating space-time defects, and construct the Burgers vector of the waves. In the context of classical continuum systems, the Burgers vector is a measure of the deformation of the medium, and at a microscopic (atomic) scale, it is a naturally quantized object. One purpose of the present article is ultimately to probe an alternative way on how to quantize plane gravitational waves.

In this work we shall study k -inflation theories with non-minimal coupling of the scalar field to gravity, in the presence of only a higher order kinetic term of the form ?�const? X μ , with X= 1 2 ??μ ? ??μ ? . The study will be focused in the cases where a scalar potential is included or is absent, and the evolution of the scalar field will be assumed to satisfy the slow-roll or the constant-roll condition. In the case of the slow-roll models with scalar potential, we shall calculate the slow-roll indices, and the corresponding observational indices of the theory, and we demonstrate that the resulting theory is compatible with the latest Planck data. The same results are obtained in the constant-roll case, at least in the presence of a scalar potential. In the case that models without potential are considered, the results are less appealing since these are strongly model dependent, and at least for a power-law choice of the non-minimal coupling, the theory is non-viable. Finally, due to the fact that the scalar and tensor power spectra are conformal invariant quantities, we argue that the Einstein frame counterpart of the non-minimal k -inflation models with scalar potential, can be a viable theory, due to the conformal invariance of the observational indices. The Einstein frame theory is more involved and thus more difficult to work with it analytically, so one implication of our work is that we provide evidence for the viability of another class of k -inflation models.

We describe a geometric and symmetry-based formulation of the equivalence principle in non-relativistic physics. It applies both on the classical and quantum levels and states that the Newtonian potential can be eliminated in favor of a curved and time-dependent spatial metric. It is this requirement that forces the gravitational mass to be equal to the inertial mass. We identify the symmetry responsible for the equivalence principle as the remnant of time-reparameterization symmetry of the relativistic theory. We also clarify the transformation properties of the Schroedinger wave-function under arbitrary changes of frame.